University of Washington - Department of Statistics
In this paper, the authors propose and investigate two new methods for achieving less bias in non-parametric regression and use simulations to compare the bias, variance, and mean squared error from the second and preferred of these two methods to the biases, variances, and mean squared errors of the local constant, local linear, and local cubic non-parametric regression estimators. The two new methods proposed by the authors have bias of order h^4 where h is the estimatorâ€™s smoothing parameter, in contrast to the basic kernel estimatorâ€™s bias of order h^2. The majority of this talk will be conceptual rather than theoretical. I will introduce the two methods and explain the subtle but important difference between them. I will briefly explain reasons for their improvement in bias followed by some simulation results and conclusions. The authors of this paper are B.U. Park, W.C. Kim, D. Ruppert, M.C. Jones, D.F. Signorini, and R. Kohn.